The Prony equation (named after
Gaspard de Prony
Baron Gaspard Clair François Marie Riche de Prony (22 July 1755 – 29 July 1839) was a French mathematician and engineer, who worked on hydraulics. He was born at Chamelet, Beaujolais, France and died in Asnières-sur-Seine, France.
Educati ...
) is a historically important equation in
hydraulics
Hydraulics (from Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very basic level, hydraulics is the liquid counte ...
, used to calculate the
head loss due to
friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction:
*Dry friction is a force that opposes the relative lateral motion of ...
within a given run of pipe. It is an
empirical equation developed by
Frenchman
The French people (french: Français) are an ethnic group and nation primarily located in Western Europe that share a common French culture, history, and language, identified with the country of France.
The French people, especially th ...
Gaspard de Prony
Baron Gaspard Clair François Marie Riche de Prony (22 July 1755 – 29 July 1839) was a French mathematician and engineer, who worked on hydraulics. He was born at Chamelet, Beaujolais, France and died in Asnières-sur-Seine, France.
Educati ...
in the 19th century:
:
where ''h
f'' is the head loss due to friction, calculated from: the ratio of the length to
diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid fo ...
of the pipe ''L/D'', the velocity of the flow ''V'', and two empirical factors ''a'' and ''b'' to account for friction.
This equation has been supplanted in modern hydraulics by the
Darcy–Weisbach equation
In fluid dynamics, the Darcy–Weisbach equation is an empirical equation that relates the head loss, or pressure loss, due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressible fluid. The equation ...
, which used it as a starting point.
References
*. The Prony equation and its replacement by the Darcy–Weisbach equation are on pp. 11–12.
Equations of fluid dynamics
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